Revisions to What's the best technique to do math calculations in my head?

deleted 3 characters in body

Source Link

edited Dec 5, 2017 at 6:49

Jasper

3.2k
14
21

When I do math in my head, I usually combine a few approaches:

Always keep track of units.
Try to re-use math I have memorized (such as the multiplication tables, powers of 2, powers of 3, common square roots, common trig ratios, et cetera)
Use "carrying" to split each number into a round number and an "error" term. Often, the first operations will be on the number(s) that are closest to round numbers.
An "error term" can either be a number (such as 2 or -4 or 0.216), or a percentage of the round number. For example, 0.3048 is 1.6% more than 0.3. In the example below, I convert "0.3048" to "0.3 (+ 1.6%)". A more standard way of writing this would be "0.3 * (1 + 1.6%)".
Use memorized values to handle round number inputs to square roots or trig functions, and interpolation to adjust for the "error" terms.
Chunk four-digit numbers into pairs of digits.
Use my fingers to store values as Roman numerals. (This allows storing a pair of digits on my hands: Right fingers = Is; right thumb = V; left fingers = Xs; left thumb = L.)

For example:

99 * 58 = (100 - 1) * 58 = 5800 - 58 = 5700 + 100 - 58 = 5742
2048 + 1296 = 2048 + 1300 - 4 = 2044 + 1300 = 3344
506 + 998 = 506 + 1000 - 2 = 504 + 1000 = 1504

Since the original poster asked (in a comment) about square roots:

$$ \sqrt{\frac{2 \cdot 0.3048 \text{ meters}}{(9.80665 \frac{\text{meters}}{\text{second}^2})}} $$ $$= \sqrt{\frac{2 \cdot 0.3048 \text{ second}^2}{9.80665}} $$ $$= 1 \text{ second} \sqrt{\frac{2 \cdot 0.3048}{9.80665}} $$ $$\approx 1 \text{ second} \sqrt{\frac{2 \cdot 0.3 (+ 1.6\%)}{10 (- 2\%)}} $$ $$\approx 1 \text{ second} \sqrt{\frac{0.6}{10} (+1.6\% +2\%)}$$ $$= 1 \text{ second} \sqrt{0.06 (+1.6\% +2\%)}$$ $$= 0.1 \text{ second} \sqrt{6 (+3.6\%)}$$ $$= 0.1 \text{ second} \sqrt{6.216}$$ $$= 0.01 \text{ second} \sqrt{621.6}$$ $$\approx 0.01 \text{ second}\cdot (\sqrt{625}-\frac{3.4}{625-576})$$ $$\approx 0.01 \text{ second}\cdot (25-\frac{3.4}{50})$$ $$= 0.01 \text{ second}\cdot (25-\frac{6.8}{100})$$ $$\approx 0.01 \text{ second}\cdot (25-0.07)$$ $$= 0.01 \text{ second}\cdot 24.93$$ $$= 0.2493 \text{ seconds}. $$ (Actual value is 0.249322 seconds, at 45 degrees45° latitude on Earth.)

When I do math in my head, I usually combine a few approaches:

Always keep track of units.
Try to re-use math I have memorized (such as the multiplication tables, powers of 2, powers of 3, common square roots, common trig ratios, et cetera)
Use "carrying" to split each number into a round number and an "error" term. Often, the first operations will be on the number(s) that are closest to round numbers.
An "error term" can either be a number (such as 2 or -4 or 0.216), or a percentage of the round number. For example, 0.3048 is 1.6% more than 0.3. In the example below, I convert "0.3048" to "0.3 (+ 1.6%)". A more standard way of writing this would be "0.3 * (1 + 1.6%)".
Use memorized values to handle round number inputs to square roots or trig functions, and interpolation to adjust for the "error" terms.
Chunk four-digit numbers into pairs of digits.
Use my fingers to store values as Roman numerals. (This allows storing a pair of digits on my hands: Right fingers = Is; right thumb = V; left fingers = Xs; left thumb = L.)

For example:

99 * 58 = (100 - 1) * 58 = 5800 - 58 = 5700 + 100 - 58 = 5742
2048 + 1296 = 2048 + 1300 - 4 = 2044 + 1300 = 3344
506 + 998 = 506 + 1000 - 2 = 504 + 1000 = 1504

Since the original poster asked (in a comment) about square roots:

$$ \sqrt{\frac{2 \cdot 0.3048 \text{ meters}}{(9.80665 \frac{\text{meters}}{\text{second}^2})}} $$ $$= \sqrt{\frac{2 \cdot 0.3048 \text{ second}^2}{9.80665}} $$ $$= 1 \text{ second} \sqrt{\frac{2 \cdot 0.3048}{9.80665}} $$ $$\approx 1 \text{ second} \sqrt{\frac{2 \cdot 0.3 (+ 1.6\%)}{10 (- 2\%)}} $$ $$\approx 1 \text{ second} \sqrt{\frac{0.6}{10} (+1.6\% +2\%)}$$ $$= 1 \text{ second} \sqrt{0.06 (+1.6\% +2\%)}$$ $$= 0.1 \text{ second} \sqrt{6 (+3.6\%)}$$ $$= 0.1 \text{ second} \sqrt{6.216}$$ $$= 0.01 \text{ second} \sqrt{621.6}$$ $$\approx 0.01 \text{ second}\cdot (\sqrt{625}-\frac{3.4}{625-576})$$ $$\approx 0.01 \text{ second}\cdot (25-\frac{3.4}{50})$$ $$= 0.01 \text{ second}\cdot (25-\frac{6.8}{100})$$ $$\approx 0.01 \text{ second}\cdot (25-0.07)$$ $$= 0.01 \text{ second}\cdot 24.93$$ $$= 0.2493 \text{ seconds}. $$ (Actual value is 0.249322 seconds, at 45 degrees latitude on Earth.)

When I do math in my head, I usually combine a few approaches:

Always keep track of units.
Try to re-use math I have memorized (such as the multiplication tables, powers of 2, powers of 3, common square roots, common trig ratios, et cetera)
Use "carrying" to split each number into a round number and an "error" term. Often, the first operations will be on the number(s) that are closest to round numbers.
An "error term" can either be a number (such as 2 or -4 or 0.216), or a percentage of the round number. For example, 0.3048 is 1.6% more than 0.3. In the example below, I convert "0.3048" to "0.3 (+ 1.6%)". A more standard way of writing this would be "0.3 * (1 + 1.6%)".
Use memorized values to handle round number inputs to square roots or trig functions, and interpolation to adjust for the "error" terms.
Chunk four-digit numbers into pairs of digits.
Use my fingers to store values as Roman numerals. (This allows storing a pair of digits on my hands: Right fingers = Is; right thumb = V; left fingers = Xs; left thumb = L.)

For example:

99 * 58 = (100 - 1) * 58 = 5800 - 58 = 5700 + 100 - 58 = 5742
2048 + 1296 = 2048 + 1300 - 4 = 2044 + 1300 = 3344
506 + 998 = 506 + 1000 - 2 = 504 + 1000 = 1504

Since the original poster asked (in a comment) about square roots:

$$ \sqrt{\frac{2 \cdot 0.3048 \text{ meters}}{(9.80665 \frac{\text{meters}}{\text{second}^2})}} $$ $$= \sqrt{\frac{2 \cdot 0.3048 \text{ second}^2}{9.80665}} $$ $$= 1 \text{ second} \sqrt{\frac{2 \cdot 0.3048}{9.80665}} $$ $$\approx 1 \text{ second} \sqrt{\frac{2 \cdot 0.3 (+ 1.6\%)}{10 (- 2\%)}} $$ $$\approx 1 \text{ second} \sqrt{\frac{0.6}{10} (+1.6\% +2\%)}$$ $$= 1 \text{ second} \sqrt{0.06 (+1.6\% +2\%)}$$ $$= 0.1 \text{ second} \sqrt{6 (+3.6\%)}$$ $$= 0.1 \text{ second} \sqrt{6.216}$$ $$= 0.01 \text{ second} \sqrt{621.6}$$ $$\approx 0.01 \text{ second}\cdot (\sqrt{625}-\frac{3.4}{625-576})$$ $$\approx 0.01 \text{ second}\cdot (25-\frac{3.4}{50})$$ $$= 0.01 \text{ second}\cdot (25-\frac{6.8}{100})$$ $$\approx 0.01 \text{ second}\cdot (25-0.07)$$ $$= 0.01 \text{ second}\cdot 24.93$$ $$= 0.2493 \text{ seconds}. $$ (Actual value is 0.249322 seconds, at 45° latitude on Earth.)

How to count using Roman numerals on one's hands.

Source Link

edited Dec 5, 2017 at 6:27

Jasper

3.2k
14
21

When I do math in my head, I usually combine a few approaches:

Always keep track of units.
Try to re-use math I have memorized (such as the multiplication tables, powers of 2, powers of 3, common square roots, common trig ratios, et cetera)
Use "carrying" to split each number into a round number and an "error" term. Often, the first operations will be on the number(s) that are closest to round numbers.
An "error term" can either be a number (such as 2 or -4 or 0.216), or a percentage of the round number. For example, 0.3048 is 1.6% more than 0.3. In the example below, I convert "0.3048" to "0.3 (+ 1.6%)". A more standard way of writing this would be "0.3 * (1 + 1.6%)".
Use memorized values to handle round number inputs to square roots or trig functions, and interpolation to adjust for the "error" terms.
Chunk four-digit numbers into pairs of digits.
Use my fingers to store values as Roman numerals. (This allows storing a pair of digits on my hands: Right fingers = Is; right thumb = V; left fingers = Xs; left thumb = L.)

For example:

99 * 58 = (100 - 1) * 58 = 5800 - 58 = 5700 + 100 - 58 = 5742
2048 + 1296 = 2048 + 1300 - 4 = 2044 + 1300 = 3344
506 + 998 = 506 + 1000 - 2 = 504 + 1000 = 1504

Since the original poster asked (in a comment) about square roots:

$$ \sqrt{\frac{2 \cdot 0.3048 \text{ meters}}{(9.80665 \frac{\text{meters}}{\text{second}^2})}} $$ $$= \sqrt{\frac{2 \cdot 0.3048 \text{ second}^2}{9.80665}} $$ $$= 1 \text{ second} \sqrt{\frac{2 \cdot 0.3048}{9.80665}} $$ $$\approx 1 \text{ second} \sqrt{\frac{2 \cdot 0.3 (+ 1.6\%)}{10 (- 2\%)}} $$ $$\approx 1 \text{ second} \sqrt{\frac{0.6}{10} (+1.6\% +2\%)}$$ $$= 1 \text{ second} \sqrt{0.06 (+1.6\% +2\%)}$$ $$= 0.1 \text{ second} \sqrt{6 (+3.6\%)}$$ $$= 0.1 \text{ second} \sqrt{6.216}$$ $$= 0.01 \text{ second} \sqrt{621.6}$$ $$\approx 0.01 \text{ second}\cdot (\sqrt{625}-\frac{3.4}{625-576})$$ $$\approx 0.01 \text{ second}\cdot (25-\frac{3.4}{50})$$ $$= 0.01 \text{ second}\cdot (25-\frac{6.8}{100})$$ $$\approx 0.01 \text{ second}\cdot (25-0.07)$$ $$= 0.01 \text{ second}\cdot 24.93$$ $$= 0.2493 \text{ seconds}. $$ (Actual value is 0.249322 seconds, at 45 degrees latitude on Earth.)

When I do math in my head, I usually combine a few approaches:

Always keep track of units.
Try to re-use math I have memorized (such as the multiplication tables, powers of 2, powers of 3, common square roots, common trig ratios, et cetera)
Use "carrying" to split each number into a round number and an "error" term. Often, the first operations will be on the number(s) that are closest to round numbers.
An "error term" can either be a number (such as 2 or -4 or 0.216), or a percentage of the round number. For example, 0.3048 is 1.6% more than 0.3. In the example below, I convert "0.3048" to "0.3 (+ 1.6%)". A more standard way of writing this would be "0.3 * (1 + 1.6%)".
Use memorized values to handle round number inputs to square roots or trig functions, and interpolation to adjust for the "error" terms.
Chunk four-digit numbers into pairs of digits.
Use my fingers to store values as Roman numerals. (This allows storing a pair of digits on my hands.)

For example:

99 * 58 = (100 - 1) * 58 = 5800 - 58 = 5700 + 100 - 58 = 5742
2048 + 1296 = 2048 + 1300 - 4 = 2044 + 1300 = 3344
506 + 998 = 506 + 1000 - 2 = 504 + 1000 = 1504

Since the original poster asked (in a comment) about square roots:

$$ \sqrt{\frac{2 \cdot 0.3048 \text{ meters}}{(9.80665 \frac{\text{meters}}{\text{second}^2})}} $$ $$= \sqrt{\frac{2 \cdot 0.3048 \text{ second}^2}{9.80665}} $$ $$= 1 \text{ second} \sqrt{\frac{2 \cdot 0.3048}{9.80665}} $$ $$\approx 1 \text{ second} \sqrt{\frac{2 \cdot 0.3 (+ 1.6\%)}{10 (- 2\%)}} $$ $$\approx 1 \text{ second} \sqrt{\frac{0.6}{10} (+1.6\% +2\%)}$$ $$= 1 \text{ second} \sqrt{0.06 (+1.6\% +2\%)}$$ $$= 0.1 \text{ second} \sqrt{6 (+3.6\%)}$$ $$= 0.1 \text{ second} \sqrt{6.216}$$ $$= 0.01 \text{ second} \sqrt{621.6}$$ $$\approx 0.01 \text{ second}\cdot (\sqrt{625}-\frac{3.4}{625-576})$$ $$\approx 0.01 \text{ second}\cdot (25-\frac{3.4}{50})$$ $$= 0.01 \text{ second}\cdot (25-\frac{6.8}{100})$$ $$\approx 0.01 \text{ second}\cdot (25-0.07)$$ $$= 0.01 \text{ second}\cdot 24.93$$ $$= 0.2493 \text{ seconds}. $$ (Actual value is 0.249322 seconds, at 45 degrees latitude on Earth.)

When I do math in my head, I usually combine a few approaches:

Always keep track of units.
Try to re-use math I have memorized (such as the multiplication tables, powers of 2, powers of 3, common square roots, common trig ratios, et cetera)
Use "carrying" to split each number into a round number and an "error" term. Often, the first operations will be on the number(s) that are closest to round numbers.
An "error term" can either be a number (such as 2 or -4 or 0.216), or a percentage of the round number. For example, 0.3048 is 1.6% more than 0.3. In the example below, I convert "0.3048" to "0.3 (+ 1.6%)". A more standard way of writing this would be "0.3 * (1 + 1.6%)".
Use memorized values to handle round number inputs to square roots or trig functions, and interpolation to adjust for the "error" terms.
Chunk four-digit numbers into pairs of digits.
Use my fingers to store values as Roman numerals. (This allows storing a pair of digits on my hands: Right fingers = Is; right thumb = V; left fingers = Xs; left thumb = L.)

For example:

99 * 58 = (100 - 1) * 58 = 5800 - 58 = 5700 + 100 - 58 = 5742
2048 + 1296 = 2048 + 1300 - 4 = 2044 + 1300 = 3344
506 + 998 = 506 + 1000 - 2 = 504 + 1000 = 1504

Since the original poster asked (in a comment) about square roots:

$$ \sqrt{\frac{2 \cdot 0.3048 \text{ meters}}{(9.80665 \frac{\text{meters}}{\text{second}^2})}} $$ $$= \sqrt{\frac{2 \cdot 0.3048 \text{ second}^2}{9.80665}} $$ $$= 1 \text{ second} \sqrt{\frac{2 \cdot 0.3048}{9.80665}} $$ $$\approx 1 \text{ second} \sqrt{\frac{2 \cdot 0.3 (+ 1.6\%)}{10 (- 2\%)}} $$ $$\approx 1 \text{ second} \sqrt{\frac{0.6}{10} (+1.6\% +2\%)}$$ $$= 1 \text{ second} \sqrt{0.06 (+1.6\% +2\%)}$$ $$= 0.1 \text{ second} \sqrt{6 (+3.6\%)}$$ $$= 0.1 \text{ second} \sqrt{6.216}$$ $$= 0.01 \text{ second} \sqrt{621.6}$$ $$\approx 0.01 \text{ second}\cdot (\sqrt{625}-\frac{3.4}{625-576})$$ $$\approx 0.01 \text{ second}\cdot (25-\frac{3.4}{50})$$ $$= 0.01 \text{ second}\cdot (25-\frac{6.8}{100})$$ $$\approx 0.01 \text{ second}\cdot (25-0.07)$$ $$= 0.01 \text{ second}\cdot 24.93$$ $$= 0.2493 \text{ seconds}. $$ (Actual value is 0.249322 seconds, at 45 degrees latitude on Earth.)

huge math formatting

Source Link

edited Dec 5, 2017 at 6:17

Jasper

3.2k
14
21

When I do math in my head, I usually combine a few approaches:

Always keep track of units.
Try to re-use math I have memorized (such as the multiplication tables, powers of 2, powers of 3, common square roots, common trig ratios, et cetera)
Use "carrying" to split each number into a round number and an "error" term. Often, the first operations will be on the number(s) that are closest to round numbers.
An "error term" can either be a number (such as 2 or -4 or 0.216), or a percentage of the round number. For example, 0.3048 is 1.6% more than 0.3. In the example below, I convert "0.3048" to "0.3 (+ 1.6%)". A more standard way of writing this would be "0.3 * (1 + 1.6%)".
Use memorized values to handle round number inputs to square roots or trig functions, and interpolation to adjust for the "error" terms.
Chunk four-digit numbers into pairs of digits.
Use my fingers to store values as Roman numerals. (This allows storing a pair of digits on my hands.)

For example:

99 * 58 = (100 - 1) * 58 = 5800 - 58 = 5700 + 100 - 58 = 5742
2048 + 1296 = 2048 + 1300 - 4 = 2044 + 1300 = 3344
506 + 998 = 506 + 1000 - 2 = 504 + 1000 = 1504

Since the original poster asked (in a comment) about square roots:

$$ \sqrt{\frac{0.3048 \cdot 2\text{ meters}^2}{(9.80665 \frac{\text{meters}}{\text{second}^2})}} $$$$ \sqrt{\frac{2 \cdot 0.3048 \text{ meters}}{(9.80665 \frac{\text{meters}}{\text{second}^2})}} $$ $$= \sqrt{0.3048 \cdot 2 \text{ second}^2 / 9.80665} $$$$= \sqrt{\frac{2 \cdot 0.3048 \text{ second}^2}{9.80665}} $$ $$= 1 \text{ second}\cdot \sqrt{\frac{0.3048 \cdot 2}{9.80665}} $$$$= 1 \text{ second} \sqrt{\frac{2 \cdot 0.3048}{9.80665}} $$ $$= 1 \text{ second}\cdot \sqrt{\frac{0.3 (+ 1.6\%) \cdot 2}{10 (- 2\%)}} $$$$\approx 1 \text{ second} \sqrt{\frac{2 \cdot 0.3 (+ 1.6\%)}{10 (- 2\%)}} $$ $$= 1 \text{ second}\cdot \sqrt{\frac{0.6}{10} +1.6\% +2\%}$$$$\approx 1 \text{ second} \sqrt{\frac{0.6}{10} (+1.6\% +2\%)}$$ $$= 0.1 \text{ second}\cdot \sqrt{6 +3.6\%}$$$$= 1 \text{ second} \sqrt{0.06 (+1.6\% +2\%)}$$ $$= 0.1 \text{ second}\cdot \sqrt{6.216}$$$$= 0.1 \text{ second} \sqrt{6 (+3.6\%)}$$ $$= 0.01 \text{ second}\cdot \sqrt{621.6}$$$$= 0.1 \text{ second} \sqrt{6.216}$$ $$= 0.01 \text{ second}\cdot \sqrt{625}-\frac{3.4}{625-576}$$$$= 0.01 \text{ second} \sqrt{621.6}$$ $$= 0.01 \text{ second}\cdot 25-\frac{3.4}{50}$$$$\approx 0.01 \text{ second}\cdot (\sqrt{625}-\frac{3.4}{625-576})$$ $$= 0.01 \text{ second}\cdot 25-\frac{6.8}{100}$$$$\approx 0.01 \text{ second}\cdot (25-\frac{3.4}{50})$$ $$= 0.01 \text{ second}\cdot 25-0.07$$$$= 0.01 \text{ second}\cdot (25-\frac{6.8}{100})$$ $$\approx 0.01 \text{ second}\cdot (25-0.07)$$ $$= 0.01 \text{ second}\cdot 24.93$$ $$= 0.2493 \text{ seconds}. $$ (Actual value is 0.249322 seconds, at 45 degrees latitude on Earth.)

When I do math in my head, I usually combine a few approaches:

Always keep track of units.
Try to re-use math I have memorized (such as the multiplication tables, powers of 2, powers of 3, common square roots, common trig ratios, et cetera)
Use "carrying" to split each number into a round number and an "error" term. Often, the first operations will be on the number(s) that are closest to round numbers.
An "error term" can either be a number (such as 2 or -4 or 0.216), or a percentage of the round number. For example, 0.3048 is 1.6% more than 0.3. In the example below, I convert "0.3048" to "0.3 (+ 1.6%)". A more standard way of writing this would be "0.3 * (1 + 1.6%)".
Use memorized values to handle round number inputs to square roots or trig functions, and interpolation to adjust for the "error" terms.
Chunk four-digit numbers into pairs of digits.
Use my fingers to store values as Roman numerals. (This allows storing a pair of digits on my hands.)

For example:

99 * 58 = (100 - 1) * 58 = 5800 - 58 = 5700 + 100 - 58 = 5742
2048 + 1296 = 2048 + 1300 - 4 = 2044 + 1300 = 3344
506 + 998 = 506 + 1000 - 2 = 504 + 1000 = 1504

Since the original poster asked (in a comment) about square roots:

$$ \sqrt{\frac{0.3048 \cdot 2\text{ meters}^2}{(9.80665 \frac{\text{meters}}{\text{second}^2})}} $$ $$= \sqrt{0.3048 \cdot 2 \text{ second}^2 / 9.80665} $$ $$= 1 \text{ second}\cdot \sqrt{\frac{0.3048 \cdot 2}{9.80665}} $$ $$= 1 \text{ second}\cdot \sqrt{\frac{0.3 (+ 1.6\%) \cdot 2}{10 (- 2\%)}} $$ $$= 1 \text{ second}\cdot \sqrt{\frac{0.6}{10} +1.6\% +2\%}$$ $$= 0.1 \text{ second}\cdot \sqrt{6 +3.6\%}$$ $$= 0.1 \text{ second}\cdot \sqrt{6.216}$$ $$= 0.01 \text{ second}\cdot \sqrt{621.6}$$ $$= 0.01 \text{ second}\cdot \sqrt{625}-\frac{3.4}{625-576}$$ $$= 0.01 \text{ second}\cdot 25-\frac{3.4}{50}$$ $$= 0.01 \text{ second}\cdot 25-\frac{6.8}{100}$$ $$= 0.01 \text{ second}\cdot 25-0.07$$ $$= 0.01 \text{ second}\cdot 24.93$$ $$= 0.2493 \text{ seconds}. $$ (Actual value is 0.249322 seconds, at 45 degrees latitude on Earth.)

When I do math in my head, I usually combine a few approaches:

Always keep track of units.
Try to re-use math I have memorized (such as the multiplication tables, powers of 2, powers of 3, common square roots, common trig ratios, et cetera)
Use "carrying" to split each number into a round number and an "error" term. Often, the first operations will be on the number(s) that are closest to round numbers.
An "error term" can either be a number (such as 2 or -4 or 0.216), or a percentage of the round number. For example, 0.3048 is 1.6% more than 0.3. In the example below, I convert "0.3048" to "0.3 (+ 1.6%)". A more standard way of writing this would be "0.3 * (1 + 1.6%)".
Use memorized values to handle round number inputs to square roots or trig functions, and interpolation to adjust for the "error" terms.
Chunk four-digit numbers into pairs of digits.
Use my fingers to store values as Roman numerals. (This allows storing a pair of digits on my hands.)

For example:

99 * 58 = (100 - 1) * 58 = 5800 - 58 = 5700 + 100 - 58 = 5742
2048 + 1296 = 2048 + 1300 - 4 = 2044 + 1300 = 3344
506 + 998 = 506 + 1000 - 2 = 504 + 1000 = 1504

Since the original poster asked (in a comment) about square roots:

$$ \sqrt{\frac{2 \cdot 0.3048 \text{ meters}}{(9.80665 \frac{\text{meters}}{\text{second}^2})}} $$ $$= \sqrt{\frac{2 \cdot 0.3048 \text{ second}^2}{9.80665}} $$ $$= 1 \text{ second} \sqrt{\frac{2 \cdot 0.3048}{9.80665}} $$ $$\approx 1 \text{ second} \sqrt{\frac{2 \cdot 0.3 (+ 1.6\%)}{10 (- 2\%)}} $$ $$\approx 1 \text{ second} \sqrt{\frac{0.6}{10} (+1.6\% +2\%)}$$ $$= 1 \text{ second} \sqrt{0.06 (+1.6\% +2\%)}$$ $$= 0.1 \text{ second} \sqrt{6 (+3.6\%)}$$ $$= 0.1 \text{ second} \sqrt{6.216}$$ $$= 0.01 \text{ second} \sqrt{621.6}$$ $$\approx 0.01 \text{ second}\cdot (\sqrt{625}-\frac{3.4}{625-576})$$ $$\approx 0.01 \text{ second}\cdot (25-\frac{3.4}{50})$$ $$= 0.01 \text{ second}\cdot (25-\frac{6.8}{100})$$ $$\approx 0.01 \text{ second}\cdot (25-0.07)$$ $$= 0.01 \text{ second}\cdot 24.93$$ $$= 0.2493 \text{ seconds}. $$ (Actual value is 0.249322 seconds, at 45 degrees latitude on Earth.)