Sure, let's go through the process of estimating the answers to each given expression by rounding each number to 1 significant figure.
### Part (a)
Given expression:
[tex]\[ \frac{763 \times 42}{82} \][/tex]
#### Step-by-Step Solution:
1. Round each number to 1 significant figure:
- [tex]\(763\)[/tex] rounds to [tex]\(800\)[/tex].
- [tex]\(42\)[/tex] rounds to [tex]\(40\)[/tex].
- [tex]\(82\)[/tex] rounds to [tex]\(80\)[/tex].
2. Substitute the rounded values into the expression:
[tex]\[ \frac{800 \times 40}{80} \][/tex]
3. Perform the multiplication in the numerator:
[tex]\[ 800 \times 40 = 32000 \][/tex]
4. Divide the result by the rounded denominator:
[tex]\[ \frac{32000}{80} = 400.0 \][/tex]
So, the estimated answer for part (a) is [tex]\( 400.0 \)[/tex].
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### Part (b)
Given expression:
[tex]\[ \frac{39 \times 52}{3.8 \times 4.9} \][/tex]
#### Step-by-Step Solution:
1. Round each number to 1 significant figure:
- [tex]\(39\)[/tex] rounds to [tex]\(40\)[/tex].
- [tex]\(52\)[/tex] rounds to [tex]\(50\)[/tex].
- [tex]\(3.8\)[/tex] rounds to [tex]\(4\)[/tex].
- [tex]\(4.9\)[/tex] rounds to [tex]\(5\)[/tex].
2. Substitute the rounded values into the expression:
[tex]\[ \frac{40 \times 50}{4 \times 5} \][/tex]
3. Perform the multiplication in the numerator and the denominator:
[tex]\[ 40 \times 50 = 2000 \][/tex]
[tex]\[ 4 \times 5 = 20 \][/tex]
4. Divide the numerator by the denominator:
[tex]\[ \frac{2000}{20} = 100.0 \][/tex]
So, the estimated answer for part (b) is [tex]\( 100.0 \)[/tex].
