Question

the image shows a set of beginning steps you can use to multiply 4.16 and 1.83. complete the sentences below that describe where to put the decimal point in the answer. round each number to the nearest whole. 4.16 is closest to and 1.83 is closest to. for an answer close to the product of the estimates, place the decimal between.

Explanation:

Step1: Round 4.16 to nearest whole

To round 4.16, look at the decimal part (0.16). Since 0.16 < 0.5, we round down. So 4.16 is closest to 4.

Step2: Round 1.83 to nearest whole

For 1.83, the decimal part is 0.83. Since 0.83 > 0.5, we round up. So 1.83 is closest to 2.

Step3: Find product of estimates

The product of the estimates (4 and 2) is \(4\times2 = 8\). Now, look at the product from the multiplication (076128, which is 76128 before decimal placement). We need to place the decimal so that the result is close to 8. The number 7.6128 is close to 8, so the decimal should be between 7 and 6 (i.e., after the first digit, making it 7.6128).

Answer:

4.16 is closest to \(\boldsymbol{4}\) and 1.83 is closest to \(\boldsymbol{2}\). For an answer close to the product of the estimates, place the decimal between \(\boldsymbol{7}\) and \(\boldsymbol{6}\) (resulting in 7.6128).