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AEstimate 0.42 x 0.064 by rounding both numbers to one significant
figure.
b) Work out the exact value of 0.42 × 0.064
Compare your answers to parts a) and b).
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Verified Answer :

GinnyAnswer

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:
\(\[ 0.4 \times 0.06 = 0.024 \]\)

So, the estimated value of \(\(0.42 \times 0.064\)\) 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:
\(\[ 0.42 \times 0.064 \]\)

To do this, multiply the numbers directly:
\(\[ 0.42 \times 0.064 = 0.02688 \]\)

So, the exact value of \(\(0.42 \times 0.064\)\) 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.

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