Question

how many significant figures do the following numbers have?

1. 626 = 3
2. 1800 = 2
3. 2.67 = 3
4. 0.30001 = 5
5. 0.004 = 1

write the answer to the following expressions and write how many significant figures it has.

1. 25.3 + 7.55 = 32.85, 4 sig figures
2. 10.900 - 4.30 = 6.60, 2 sig figures
3. 2.0 x 15.0 = 30, 1 sig fig
4. 24.0/6.0 = 4, 1 sig fig
5. 35.0 x 2.000 = 70, 1 sig fig
6. 16.4 + 12.87 = 29.27, 4 sig fig
7. 0.056 x 100 = 5.6, 2 significant figures

Explanation:

Step1: Recall significant - figure rules

Non - zero digits are always significant. Zeros between non - zero digits are significant. Leading zeros (zeros before non - zero digits) are not significant. Trailing zeros in a number without a decimal point may or may not be significant, but trailing zeros in a number with a decimal point are significant.

Step2: Analyze individual numbers

For 626

All three digits are non - zero, so it has 3 significant figures.

For 1800

The trailing zeros are not significant as there is no decimal point, so it has 2 significant figures.

For 2.67

All three digits are non - zero, so it has 3 significant figures.

For 0.30001

The leading zero is not significant, but the remaining five digits are significant, so it has 5 significant figures.

For 0.004

The leading zeros are not significant, and only the 4 is significant, so it has 1 significant figure.

Step3: Analyze arithmetic expressions

For 25.3 + 7.55 = 32.85

In addition, the result should be reported to the same number of decimal places as the number with the least number of decimal places in the values being added. 25.3 has one decimal place and 7.55 has two decimal places. The result 32.85 has 4 significant figures.

For 10.900−4.30 = 6.60

In subtraction, the result should be reported to the same number of decimal places as the number with the least number of decimal places in the values being subtracted. 10.900 has three decimal places and 4.30 has two decimal places. The result 6.60 has 3 significant figures (the trailing zero after the decimal is significant).

For 2.0×15.0 = 30.

In multiplication, the result should have the same number of significant figures as the number with the least number of significant figures among the values being multiplied. 2.0 has 2 significant figures and 15.0 has 3 significant figures. The result 30. (with a decimal point) has 2 significant figures.

For 24.0/6.0 = 4.

In division, the result should have the same number of significant figures as the number with the least number of significant figures among the values being divided. 24.0 has 3 significant figures and 6.0 has 2 significant figures. The result 4. has 1 significant figure.

For 35.0×2.000 = 70.

35.0 has 3 significant figures and 2.000 has 4 significant figures. The result 70. (with a decimal point) has 2 significant figures.

For 16.4 + 12.87 = 29.27

16.4 has one decimal place and 12.87 has two decimal places. The result 29.27 has 4 significant figures.

For 0.056×100 = 5.6

0.056 has 2 significant figures and 100 (as a multiplier in this context) is considered exact. The result 5.6 has 2 significant figures.

Answer:

1. 626: 3 significant figures
2. 1800: 2 significant figures
3. 2.67: 3 significant figures
4. 0.30001: 5 significant figures
5. 0.004: 1 significant figure
6. 25.3 + 7.55 = 32.85, 4 significant figures
7. 10.900−4.30 = 6.60, 3 significant figures
8. 2.0×15.0 = 30., 2 significant figures
9. 24.0/6.0 = 4., 1 significant figure
10. 35.0×2.000 = 70., 2 significant figures
11. 16.4 + 12.87 = 29.27, 4 significant figures
12. 0.056×100 = 5.6, 2 significant figures