Introduction:
To find the product of the place value of 7 in 726.423 and the place value of 7 in 16.075, we need to understand the concept of place value and how it relates to multiplying numbers.

Place Value:
Place value is the value of a digit based on its position in a number. Each digit in a number has a specific place value, which determines its worth. The place value of a digit increases from right to left, with the rightmost digit being in the ones place.

Decimals:
Decimals are a way to represent numbers that are less than one or whole numbers. The digits to the right of the decimal point represent fractions of a whole. The place value of the digits to the right of the decimal point follows a pattern of tenths, hundredths, thousandths, and so on.

Finding the Place Value:
To find the place value of a digit in a number, we look at its position relative to the decimal point. In 726.423, the digit 7 is in the hundreds place because it is three places to the left of the decimal point.

Multiplying the Place Values:
To find the product of the place value of 7 in 726.423 and the place value of 7 in 16.075, we need to multiply the place values of both numbers.

The place value of 7 in 726.423 is in the hundreds place, which is 100 times greater than the ones place. Therefore, the place value of 7 in 726.423 is 7 * 100 = 700.

The place value of 7 in 16.075 is in the tenths place, which is 1/10th of the ones place. Therefore, the place value of 7 in 16.075 is 7 * 1/10 = 7/10.

Calculating the Product:
To find the product of the place values, we multiply 700 by 7/10:

700 * 7/10 = (700 * 7) / 10 = 4900 / 10 = 490

Therefore, the product of the place value of 7 in 726.423 and the place value of 7 in 16.075 is 490.

Summary:
To find the product of the place value of 7 in 726.423 and the place value of 7 in 16.075, we determined the place values of both digits and then multiplied them. The place value of 7 in 726.423 is 700, and the place value of 7 in 16.075 is 7/10. Multiplying these values gives us a product of 490.

700000 70