How many decimal places do you think are in the product of 1.2 × 1.43 × 0.3? What strategy did you use to make your prediction? Multiply to check your prediction.
Understand the Problem
The question is asking about determining the number of decimal places in the product of three numbers and the strategy used for making the prediction. It involves multiplication of decimals and understanding the rules governing decimal placement.
Answer
The product has 4 decimal places.
Answer for screen readers
The product of $1.2 \times 1.43 \times 0.3$ has 4 decimal places.
Steps to Solve
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Count the decimal places in each number
To find the total number of decimal places in the product, first identify the decimal places in each number.
- $1.2$ has 1 decimal place.
- $1.43$ has 2 decimal places.
- $0.3$ has 1 decimal place.
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Sum the decimal places
Add the decimal places from each of the numbers together to find the total.
$$ 1 + 2 + 1 = 4 $$ -
Conclusion regarding the product
The product of these numbers will have a total of 4 decimal places. -
Verification by multiplication
To verify, multiply the numbers together:
- First, multiply $1.2 \times 1.43$ resulting in $1.716$.
- Then, multiply $1.716 \times 0.3$.
$$ 1.716 \times 0.3 = 0.5148 $$
Counting the decimal places in $0.5148$, we confirm that there are indeed 4 decimal places.
The product of $1.2 \times 1.43 \times 0.3$ has 4 decimal places.
More Information
This answer illustrates how to count decimal places effectively and confirms the prediction through actual multiplication. Understanding the decimal placement helps in rounding and estimating products without direct calculation.
Tips
- Miscounting decimal places: Ensure you carefully count the number of decimal places in each factor.
- Forgetting to sum the decimal places: Always remember to add the decimal counts together before concluding.
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