Question

how many significant digits do the following numbers contain?

1. 347.09
2. 0.009
3. 3,000,000
4. 1001000
5. 0.000080

round the following numbers to two significant digits

1. 87.573
2. 4.3691×10^8
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. 859.00×2000
5. (3.0×10^3 + 8.0×10^4)×120

Explanation:

Step1: Determine significant - digits 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: Find significant digits for 347.09

Non - zero digits 3, 4, 7 and trailing zero after decimal and 9 are significant. So, there are 5 significant digits.

Step3: Find significant digits for 0.009

Leading zeros are not significant. Only 9 is significant, so 1 significant digit.

Step4: Find significant digits for 3,000,000

Trailing zeros without decimal may not be significant. Assuming no other context, 1 significant digit.

Step5: Find significant digits for 1001000

Zeros between non - zero digits are significant. There are 7 significant digits.

Step6: Find significant digits for 0.000080

Leading zeros are not significant, but the trailing zero after 8 is significant. So, 2 significant digits.

Step7: Round 87.573 to two significant digits

Look at the third digit. Since 5 or greater, round up. 88.

Step8: Round 43691×10⁸ to two significant digits

First, write in scientific notation as 4.3691×10¹². Look at the third digit 6, round up. 4.4×10¹².

Step9: Round 0.01852 to two significant digits

Leading zeros not significant. Look at third digit 5, round up. 0.019.

Step10: Round 9000 to two significant digits

9000 (assuming no decimal), in scientific notation 9.0×10³.

Step11: Round 629.55 to two significant digits

Look at third digit 9, round up. 630.

Step12: Calculate 61.20 + 9.35+80

61.20+9.35 = 70.55, 70.55 + 80=150.55. For addition, round to the least number of decimal places. 80 has no decimal places, so 150.

Step13: Calculate 12000 - 999

12000−999 = 11001. For subtraction, same rule as addition for decimal - places. 12000 has no decimal places, so 11000.

Step14: Calculate 6543.2÷620

6543.2÷620 = 10.553548. For division, round to the least number of significant digits. 620 has 2 significant digits, so 11.

Step15: Calculate 859.00×2000

859.00×2000 = 1718000. 2000 has 1 significant digit, so 2000000.

Step16: Calculate (3.0×10³+8.0×10⁴)×120

3.0×10³ = 3000, 8.0×10⁴ = 80000, 3000 + 80000=83000, 83000×120 = 9960000. 3.0 and 8.0 have 2 significant digits, 120 has 2 significant digits, so 1.0×10⁷.

Answer:

1. 5
2. 1
3. 1
4. 7
5. 2
6. 88
7. 4.4×10¹²
8. 0.019
9. 9.0×10³
10. 630
11. 150
12. 11000
13. 11
14. 2000000
15. 1.0×10⁷