Problem 20 - Prealgebra

Question

Give the place value of the 5 in each of the following numbers. $$25.92$$

Step-by-Step Solution

Answer

The place value of 5 in 25.92 is 50.

Step 1: Identify the Position of 5

First, identify the position of the digit 5 in the number 25.92. The digit 5 is in the tens place in the entire number structure.

Step 2: Determine the Place Value

The place value of a digit is determined by the position it occupies. Since the 5 is in the tens place, its place value is calculated as \(5 \times 10 = 50\).

Key Concepts

Tens Place

In any number, the tens place holds significant value. It's the position right after the hundreds place and before the units place. This position tells us how many groups of ten are within a number. For instance, in the number 25.92, the digit 5 is in the tens place, which is pivotal in understanding its total value contribution. To determine its value, we multiply by 10: hence, the place value of 5 is 5 times 10, which equals 50. This calculation shows how many 'tens' are part of the whole number, painting a clear picture of its contribution to the magnitude of the number.

Decimal Numbers

Decimal numbers are numbers that have a decimal point, which separates the whole number from the fractional part of the number. In 25.92, 25 is the whole number part, and 92 is the fractional part. They are fundamental in understanding more minute and precise value assignments.

• The number to the left of the decimal (25) holds most of the value when thinking of magnitude or size.
• The numbers to the right (92) represent portions of a whole, essentially bringing in accuracy.
• When considering place value, both parts are crucial, depending upon which digit we focus on.

This representation helps us understand the value of each digit more thoroughly and ensures proper mathematical calculations.

Digit Position

Every digit in a number has a specific position and contributes variably depending on its place. The position of a digit tells us its multiplier — how much weight or value it carries in the full number.

• Units place (or ones place): It multiplies the digit by 1.
• Tens place: Multiplies the digit by 10.
• Hundreds place and beyond: Multiplies by powers of 10 based on how many places to the left it is from the decimal.

For digits in the fractional part of a decimal, positions take values like tenths, hundredths, etc., and they carry the concept of division by powers of 10. Understanding digit positions effectively demands noting whether they are to the left or right of the decimal, as this determines how they combine to form the complete number.