Answer :
Certainly! Let's solve the problem step by step.
### a) Estimate 0.42 × 0.064 by rounding both numbers to one significant figure.
To round to one significant figure:
- 0.42: The first non-zero digit is 4. The next digit is 2.
- Since 2 is less than 5, we round down to 0.4.
- 0.064: The first non-zero digit is 6. The next digit is 4.
- Since 4 is less than 5, we round down to 0.06.
Now multiply the rounded values:
[tex]\[ 0.4 \times 0.06 = 0.024 \][/tex]
So, the estimated value of [tex]\(0.42 \times 0.064\)[/tex] by rounding to one significant figure is 0.024.
### b) Work out the exact value of 0.42 × 0.064.
Now let's calculate the exact value:
[tex]\[ 0.42 \times 0.064 \][/tex]
To do this, multiply the numbers directly:
[tex]\[ 0.42 \times 0.064 = 0.02688 \][/tex]
So, the exact value of [tex]\(0.42 \times 0.064\)[/tex] is 0.02688.
### Comparison
- The estimated value when rounded to one significant figure is 0.024.
- The exact value is 0.02688.
Comparison: The estimated value (0.024) is slightly less than the exact value (0.02688). This is because the rounding down of both numbers resulted in a product that is a bit smaller than the actual product. However, the estimation is relatively close to the exact value, considering the significant figures used in the approximation.
### a) Estimate 0.42 × 0.064 by rounding both numbers to one significant figure.
To round to one significant figure:
- 0.42: The first non-zero digit is 4. The next digit is 2.
- Since 2 is less than 5, we round down to 0.4.
- 0.064: The first non-zero digit is 6. The next digit is 4.
- Since 4 is less than 5, we round down to 0.06.
Now multiply the rounded values:
[tex]\[ 0.4 \times 0.06 = 0.024 \][/tex]
So, the estimated value of [tex]\(0.42 \times 0.064\)[/tex] by rounding to one significant figure is 0.024.
### b) Work out the exact value of 0.42 × 0.064.
Now let's calculate the exact value:
[tex]\[ 0.42 \times 0.064 \][/tex]
To do this, multiply the numbers directly:
[tex]\[ 0.42 \times 0.064 = 0.02688 \][/tex]
So, the exact value of [tex]\(0.42 \times 0.064\)[/tex] is 0.02688.
### Comparison
- The estimated value when rounded to one significant figure is 0.024.
- The exact value is 0.02688.
Comparison: The estimated value (0.024) is slightly less than the exact value (0.02688). This is because the rounding down of both numbers resulted in a product that is a bit smaller than the actual product. However, the estimation is relatively close to the exact value, considering the significant figures used in the approximation.
