Answer :
Sure, let's solve the given problems step-by-step by estimating the values.
### Part (a)
Estimate the value of [tex]\( 50.25 \times 0.49 \)[/tex]
1. Round the numbers to simpler values:
- [tex]\( 50.25 \approx 50 \)[/tex] (round to the nearest integer)
- [tex]\( 0.49 \approx 0.5 \)[/tex] (round to the nearest tenth)
2. Multiply the rounded values:
[tex]\[
50 \times 0.5 = 25
\][/tex]
So, the estimated value of [tex]\( 50.25 \times 0.49 \)[/tex] is 25.
### Part (b)
Estimate the value of [tex]\( 197 \div 0.399 \)[/tex]
1. Round the numbers to simpler values:
- [tex]\( 197 \approx 200 \)[/tex] (round to the nearest hundred)
- [tex]\( 0.399 \approx 0.4 \)[/tex] (round to the nearest tenth)
2. Divide the rounded values:
[tex]\[
\frac{200}{0.4} = 200 \div 0.4 = 200 \times \frac{10}{4} = 200 \times 2.5 = 500
\][/tex]
So, the estimated value of [tex]\( 197 \div 0.399 \)[/tex] is 500.
### Summary
- The estimated value of [tex]\( 50.25 \times 0.49 \)[/tex] is 25.
- The estimated value of [tex]\( 197 \div 0.399 \)[/tex] is 500.
### Part (a)
Estimate the value of [tex]\( 50.25 \times 0.49 \)[/tex]
1. Round the numbers to simpler values:
- [tex]\( 50.25 \approx 50 \)[/tex] (round to the nearest integer)
- [tex]\( 0.49 \approx 0.5 \)[/tex] (round to the nearest tenth)
2. Multiply the rounded values:
[tex]\[
50 \times 0.5 = 25
\][/tex]
So, the estimated value of [tex]\( 50.25 \times 0.49 \)[/tex] is 25.
### Part (b)
Estimate the value of [tex]\( 197 \div 0.399 \)[/tex]
1. Round the numbers to simpler values:
- [tex]\( 197 \approx 200 \)[/tex] (round to the nearest hundred)
- [tex]\( 0.399 \approx 0.4 \)[/tex] (round to the nearest tenth)
2. Divide the rounded values:
[tex]\[
\frac{200}{0.4} = 200 \div 0.4 = 200 \times \frac{10}{4} = 200 \times 2.5 = 500
\][/tex]
So, the estimated value of [tex]\( 197 \div 0.399 \)[/tex] is 500.
### Summary
- The estimated value of [tex]\( 50.25 \times 0.49 \)[/tex] is 25.
- The estimated value of [tex]\( 197 \div 0.399 \)[/tex] is 500.
