QuestionIdentify significant figures in these values and round the numbers as indicated:
1. a) 1,234, b) 0.023, c) 890, d) 0.000120, e) 1090.0010, f) \9.010 \times 10^{-2}$, h) 1,000.
2. Round: a) , b) , c) 34 (1), d) 0.0047845 (3), e) 0.0399985 (2), f) \$0.0354800(5)\$.
Studdy Solution
STEP 1
Assumptions1. We understand what significant figures are they are the digits in a number that carry meaningful information about its precision.
. We know how to identify significant figures all non-zero digits are significant, zeroes between non-zero digits are significant, leading zeroes are not significant, trailing zeroes are significant only if they are after a decimal point.
3. We know how to round numbers to a certain number of significant figures if the digit after the last significant figure is greater than or equal to5, we round up; if it's less than5, we round down.
STEP 2
Let's identify the significant figures in each of the given values.
a)1,234All non-zero digits are significant.
b)0.023Leading zeroes are not significant, so only the2 and are significant.
c)890All non-zero digits are significant. The trailing zero is not after a decimal point, so it is not significant.
d)0.000120Leading zeroes are not significant, so only the1,2 and0 are significant. The trailing zero is after a decimal point, so it is significant.
e)1090.0010All non-zero digits are significant. The zeroes between non-zero digits are significant. The trailing zero is after a decimal point, so it is significant.
f)
All non-zero digits are significant. The zeroes between non-zero digits are significant.
g)
All non-zero digits are significant. The zeroes between non-zero digits are significant. The trailing zero is after a decimal point, so it is significant.
h)1,000All non-zero digits are significant. The trailing zeroes are not after a decimal point, so they are not significant.
STEP 3
Now let's round each number to the amount of significant figures indicated.
a) The fourth significant figure is8 and the digit after it is9 which is greater than5, so we round up. The rounded number is215.9.
b) The third significant figure is and the digit after it is5 which is equal to5, so we round up. The rounded number is34500.
c)34 (1)
The first significant figure is3 and the digit after it is which is less than5, so we don't round up. The rounded number is30.
d) .0047845 (3)
The third significant figure is7 and the digit after it is8 which is greater than5, so we round up. The rounded number is0.00479.
e) .0399985 (2)
The second significant figure is3 and the digit after it is9 which is greater than5, so we round up. The rounded number is0.040.
f) The fifth significant figure is8 and the digit after it is0 which is less than5, so we don't round up. The rounded number is0.03548.
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