significant figures part ii: calculations. objectives when you complete this presentation, you will...

Significant Figures

Part II: Calculations

Objectives

• When you complete this presentation, you will be able to– determine the number of significant figures in a

calculated answer

Introduction

• We know how to determine the number of significant figures in a measurement.– 3.442 g has 4 significant figures– 0.0025 m has 2 significant figures– 140 s has 2 significant figures– 0.000420 mL has 3 significant figures

• Now, we need to learn how to use those measurements in calculations.

Rounding

• In general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated.

• The calculated value must be rounded to make it consistent with the measurements.

Rounding

• To round, we need to determine how many significant figures the answer needs to have.– This depends on the measurements and the math

process used to determine the answer.– We will cover the details of that later in the

presentation.• First, let’s practice rounding numbers to a

proper number of significant figures.

Rounding

• How do we round a numerical value?• We use the same rules we have always used.– If the digit to the immediately to the right of the

last significant digit is less than 5, we drop the rest of the digits and the value of the last significant digit remains the same.

Round 45.244 to 3 sig figs 45.2➠ 44 45.2➠Round 0.85321 to 2 sig figs 0.85➠ 321 0.85➠

Rounding

• How do we round a numerical value?• We use the same rules we have always used.– If the digit to the immediately to the right of the

last significant digit is 5 or greater we drop the rest of the digits and the value of the last significant digit is increased by 1.

Round 62.557 to 3 sig figs 62.5➠ 57 62.6➠Round 0.0545 to 2 sig figs 0.054➠ 5 0.055➠

Rounding

Example 1: Round each of the following numbers to the indicated number of significant figures:1. 54,525.99 m to 3 sig figs2. 0.00741554 kg to 4 sig figs3. 37.255 s to 1 sig fig4. 0.78245 cm to 2 sig figs5. 355,000 km to 2 sig figs6. 0.0382574925 L to 3 sig figs

54,500 m0.007146 kg

40 s0.78 cm

360,000 km0.0383 L

Calculations – addition and subtraction

• The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places.

• For example: 12.52 m+ 349.0 m+ 8.24 m

369.76 m

The 349.0 m measurement has the least number of decimal places.

Calculations – addition and subtraction

• The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places.

• For example: 12.52 m+ 349.0 m+ 8.24 m

369.76 m

That measurement will control the number of decimal places in the answer.

Calculations – addition and subtraction

• The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places.

• For example: 12.52 m+ 349.0 m+ 8.24 m

369.76 m

The reported answer should be369.8 m

Calculations – addition and subtraction

Example 2: Perform each operation. Express the answer in the correct number of sig figs.1. 61.2 m + 9.35 m + 8.6 m2. 14.2 g + 8.73 g + 0.912 g3. 35 s + 72.1 s + 1.876 s4. 9.44 kg – 2.11 kg5. 1.36 cm + 10.17 cm6. 34.61 mL – 17.3 mL

79.2 m23.8 g109 s

7.33 kg11.53 cm

17.3 mL

Calculations – multiplication and division

• The answer to a multiplication or division calculation should be rounded to the same number of significant digits as the measurement with the least number of significant digits.

• For example: 7.55 m× 0.34 m

2.567 m2

The 0.34 m measurement has the least number of significant digits (2).

Calculations – multiplication and division

• The answer to a multiplication or division calculation should be rounded to the same number of significant digits as the measurement with the least number of significant digits.

• For example: 7.55 m× 0.34 m

2.567 m2

That measurement will control the number of decimal places in the answer.

Calculations – multiplication and division

• The answer to a multiplication or division calculation should be rounded to the same number of significant digits as the measurement with the least number of significant digits.

• For example: 7.55 m× 0.34 m

2.567 m2

The reported answer should be2.6 m2

Calculations – multiplication and division

Example 3: Perform each operation. Express the answer in the correct number of sig figs.1. 2.10 m × 0.70 m2. 2.4526 kg ÷ 8.43. 8.3 m × 2.22 m4. 8432 kg ÷ 12.55. 32 s × 15.1256. 34.61 mL ÷ 17.3

1.5 m2

0.29 kg18 m2

675 kg480 s

2.00 mL

Summary

• A calculated answer cannot be more precise than the least precise measurement from which it was calculated.

• The calculated value must be rounded to make it consistent with the measurements.

Summary

• Rules for rounding:– If the digit to the immediately to the right of the

last significant digit is less than 5, we drop the rest of the digits and the value of the last significant digit remains the same.

– If the digit to the immediately to the right of the last significant digit is 5 or greater we drop the rest of the digits and the value of the last significant digit is increased by 1.

Summary

• Significant figures in calculations:– The answer to an addition or subtraction

calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places.

– The answer to a multiplication or division calculation should be rounded to the same number of significant digits as the measurement with the least number of significant digits.