Question

how many significant digits do the following numbers contain?

1. 347.09
2. 0.009
3. 3,000,000
4. 100.1000
5. 0.000080

round the following numbers to two significant digits

1. 87573
2. 4.1691x10^8
3. 0.01852
4. 9000
5. 629.55

perform each operation. express your answers to the correct number of significant figures

1. 61.20 + 9.35 + 80
2. 12,000 - 999
3. 6543.2÷620
4. 859.00x2000
5. (3.0x10^3 + 8.0x10^4)x120

Explanation:

Step1: Determine significant - digits for 347.09

Non - zero digits and zeros between non - zero digits are significant. So, 347.09 has 5 significant digits.

Step2: Determine significant - digits for 0.009

Leading zeros are not significant. So, 0.009 has 1 significant digit.

Step3: Determine significant - digits for 3,000,000

Trailing zeros in a whole number without a decimal point may or may not be significant. Assuming no other context, it has 1 significant digit.

Step4: Determine significant - digits for 100.1000

Non - zero digits, zeros between non - zero digits, and trailing zeros after a decimal point are significant. So, 100.1000 has 7 significant digits.

Step5: Determine significant - digits for 0.000080

Leading zeros are not significant, but the trailing zero after the non - zero digit is significant. So, 0.000080 has 2 significant digits.

Step6: Round 87573 to two significant digits

The first two significant digits are 87. The next digit is 5, so we round up. 87573 rounds to 88000 (in scientific notation \(8.8\times 10^{4}\)).

Step7: Round \(4.1691\times 10^{8}\) to two significant digits

The first two significant digits are 4.1. The next digit is 6, so we round up. It rounds to \(4.2\times 10^{8}\).

Step8: Round 0.01852 to two significant digits

The first two significant digits are 0.018. The next digit is 5, so we round up. It rounds to 0.019.

Step9: Round 9000 to two significant digits

Assuming no other context, we write it in scientific notation. 9000 rounds to \(9.0\times 10^{3}\).

Step10: Round 629.55 to two significant digits

The first two significant digits are 62. The next digit is 9, so we round up. It rounds to 630 (in scientific notation \(6.3\times 10^{2}\)).

Step11: Calculate \(61.20 + 9.35+80\)

First, add the numbers: \(61.20 + 9.35=70.55\), then \(70.55 + 80 = 150.55\). The number 80 has the least precision (no decimal places), so the answer should be rounded to the nearest whole number. The answer is 151.

Step12: Calculate \(12000 - 999\)

\(12000-999 = 11001\). Since 12000 has the least precision (no decimal places), the answer is 11000.

Step13: Calculate \(6543.2\div620\)

\(6543.2\div620=\frac{6543.2}{620}=10.553548\). 620 has 2 significant digits, so the answer is \(11\).

Step14: Calculate \(859.00\times2000\)

\(859.00\times2000 = 1718000\). 2000 has 1 significant digit, so the answer is \(1.7\times 10^{6}\).

Step15: Calculate \((3.0\times 10^{3}+8.0\times 10^{4})\times120\)

First, add \(3.0\times 10^{3}+8.0\times 10^{4}=3000 + 80000=83000=8.3\times 10^{4}\). Then, \((8.3\times 10^{4})\times120 = 8.3\times10^{4}\times1.2\times 10^{2}=9.96\times 10^{6}\). Rounding to two significant digits, the answer is \(1.0\times 10^{7}\).

Answer:

1. 5
2. 1
3. 1
4. 7
5. 2
6. \(8.8\times 10^{4}\)
7. \(4.2\times 10^{8}\)
8. 0.019
9. \(9.0\times 10^{3}\)
10. \(6.3\times 10^{2}\)
11. 151
12. 11000
13. 11
14. \(1.7\times 10^{6}\)
15. \(1.0\times 10^{7}\)