Question

Use a calculator to evaluate the expression. Round your answer to two decimal places. $$(-7.39)(4.41)(-2.9)$$

Short answer

The solution to the given expression, rounded to two decimal places, is \[90.29\].

Step-by-step solution

Multiplication

Multiply the three numbers. In this case, the multiplication is (-7.39)(4.41)(-2.9). Don't forget that the product of an even number of negative numbers is positive.

Rounding

Once you have the result from the multiplication, round the answer to two decimal places. Remember, if the number in the third decimal place is 5 or greater, the second decimal place goes up by one.

Key concepts

Multiplication of Decimals

Understanding how to multiply decimals is crucial in math and in practical scenarios like measuring areas or calculating prices. To multiply decimals, follow the procedure you use for whole numbers, but then count and place the decimal point in the final product.

Begin by ignoring the decimal points and multiplying the numbers as if they were whole numbers. Once you've gotten your product, count the total number of decimal places in the original numbers. For instance, in the expression \( -7.39 \times 4.41 \times -2.9 \), there are a combined five decimal places — two from -7.39, two from 4.41 and one from -2.9.

After you've computed the multiplication as whole numbers, place the decimal point in the product so that it has the same total number of decimal places as your factors. Remember, the rule of signs is important here: the product of an even number of negative numbers is positive, while an odd number results in a negative.

Rounding Decimals

Rounding decimals is a valuable skill that simplifies numbers to make them easier to work with or understand. When rounding to two decimal places, you need to look at the third decimal place to decide whether to round the second decimal place up or leave it as is.

If the third decimal digit is 5 or higher, you increase the second decimal place by one. Conversely, if it's 4 or lower, the second decimal place stays the same. For instance, if you have a result like 21.345, since the third decimal place is 5, you would round the number to 21.35. However, if the result was 21.342, with the third decimal place being 4, you would round down, leaving the rounded number as 21.34.

Remember to also consider the overall value: if the original number is negative, rounding up means going closer to zero — the absolute value becomes smaller.

Negative Number Operations

Operations with negative numbers follow specific rules that are essential to understand to evaluate expressions correctly.

The most fundamental rule is that the product of two negative numbers is a positive number. This rule applies because a negative number is an additive inverse of a positive number, so multiplying two inverses results in a return to positive. In the context of the given expression \( (-7.39)(4.41)(-2.9) \), we have two negative numbers, so their product will be positive.

When dealing with multiple negative numbers, it's important to count them: an odd count will result in a negative product, whereas an even count will result in a positive product. This holds true for any number of negatives in the sequence, making it a reliable and straightforward way to determine the sign of your final product when doing both simple and complex calculations.