Sure! Let's simplify the expression [tex]\( 47.58 - 6.4 \)[/tex] using the rules of significant figures. Here’s a step-by-step solution:
1. Identify the decimal places in each number:
- The number [tex]\( 47.58 \)[/tex] has two decimal places.
- The number [tex]\( 6.4 \)[/tex] has one decimal place.
2. Perform the subtraction:
- Subtract [tex]\( 6.4 \)[/tex] from [tex]\( 47.58 \)[/tex]:
[tex]\[
47.58 - 6.4 = 41.18
\][/tex]
3. Determine the number of decimal places for the result:
- According to the rules of significant figures for addition and subtraction, the result should be rounded to the least number of decimal places in any of the numbers being combined.
- In this case, [tex]\( 6.4 \)[/tex] has the least number of decimal places (one decimal place).
4. Round the result to the appropriate number of decimal places:
- The unrounded result is [tex]\( 41.18 \)[/tex].
- Round [tex]\( 41.18 \)[/tex] to one decimal place:
[tex]\[
41.18 \approx 41.2
\][/tex]
5. Final simplified result:
- The simplified result of the expression [tex]\( 47.58 - 6.4 \)[/tex] is [tex]\( 41.2 \)[/tex].
So, using the rules of significant figures, the simplified result of [tex]\( 47.58 - 6.4 \)[/tex] is [tex]\( 41.2 \)[/tex].
