Question

Tell the nearest hundredths of a meter that each given measurement is between. Imagine you are playing Guess My Number and have narrowed the possibilities to a number between 9.9 and \(10 .\) What are three possibilities for the number?

Short answer

9.91, 9.95, 9.99

Step-by-step solution

Understand the range

The number is known to be between 9.9 and 10.0. This means any number greater than or equal to 9.9 and less than or equal to 10.0 is a possible candidate.

Identify the range of decimal values

The important decimal places to consider are the hundredths place. We need numbers between 9.90 and 10.00 that differ by a hundredth.

Determine possible numbers

Three possible numbers between 9.90 and 10.00 are: 9.91, 9.95, and 9.99. These are rounded to the nearest hundredth place and fit within the given range.

Key concepts

Understanding Decimal Places

To grasp the basics of rounding and range identification, it's crucial to understand decimal places. A decimal place is the position of a number to the right of the decimal point. For example, in the number 9.95, the '9' to the right of the decimal point is in the tenths place, and the '5' is in the hundredths place. When we talk about rounding to the nearest hundredth, we focus on the second digit after the decimal point. If this digit is 5 or higher, we round up. If it's lower, we round down. So, rounding 9.954 to the nearest hundredth gives us 9.95, while rounding 9.956 gives us 9.96.

Range Identification in Decimals

Identifying a range involves knowing the smallest and largest numbers in that span. In our exercise, we look at numbers between 9.9 and 10.0. Here, 9.9 is the lower limit, and 10.0 is the upper limit. This means any number starting from 9.9 up to 10.0 is included in the range. When we narrow it to the hundredths place, we include numbers like 9.91, 9.95, and 9.99. These numbers all fall within the given range. Practicing this helps sharpen your skills in identifying precise decimal ranges.

Using a Number Line for Range Identification

A number line is a visual tool to understand the range and placement of numbers. In our exercise, a number line from 9.90 to 10.00 can be helpful. By marking points like 9.91, 9.95, and 9.99 on the number line, you can easily identify numbers within the specified range. Visualizing this on a number line helps you see exactly where each number falls, making it clearer to choose possible numbers that fit the criteria given, matching our task to round to the nearest hundredth.