Problem 23 - Calculate With Confidence

Question

Express the following decimals to the nearest tenth. 0.13 _____

Step-by-Step Solution

Answer

The decimal 0.13 rounded to the nearest tenth is 0.1.

Step 1: Identify the decimal point

The number given is 0.13. The position of the decimal point is between the '0' and the '1', indicating tenths and hundredths places.

Step 2: Identify the tenths and hundredths digits

In 0.13, the tenths digit is '1' (the first number after the decimal), and the hundredths digit is '3' (the second number after the decimal).

Step 3: Determine rounding based on the hundredths digit

Decide whether to round the tenths digit up or keep it the same based on the hundredths digit. If the hundredths digit is 5 or greater, round up. Here, the hundredths digit is '3', which is less than 5.

Step 4: Round to the nearest tenth

Since the hundredths digit '3' is less than 5, the tenths digit remains '1'. Thus, 0.13 rounded to the nearest tenth is 0.1.

Key Concepts

Decimal Places

Understanding decimal places is crucial for dealing with numbers that aren't whole. Decimal places show digits that come after the decimal point in a number. These digits represent fractional parts of the whole number.

The first digit right after the decimal point is the 'tenths' place, and then you have the 'hundredths', 'thousandths', and so on. For instance, in the number 0.13, '1' is in the tenths place, and '3' is in the hundredths place.

• Tenths: The first digit after the decimal point.
• Hundredths: The second digit after the decimal point.
• Thousandths: The third digit after the decimal point.

Learning these placements helps in understanding how big or small a fraction of a number you are dealing with.

Rounding Rules

Rounding is a method used to simplify numbers, making them easier to work with. Rounding rules help decide if a number should be 'rounded up' or kept the same. They rely heavily on the digits following the one you want to round to.

Here's a simple rule of thumb:

• If the following digit is 5 or greater, increase the current digit by 1.
• If it's less than 5, keep the current digit the same.

Applying these rules ensures consistency in how numbers are rounded, which is critical in estimating or simplifying figures in practical situations.

Tenth Place

The tenth place plays a significant role when it comes to rounding numbers to the nearest tenth. It's the first digit right after the decimal point and determines the size of the tenth fraction of a number.

For example, consider the number 0.13. The tenths place is represented by '1'. To round 0.13 to the nearest tenth, look at the hundredths place, which is '3'.

• If this number (in the hundredths place) were 5 or greater, you would round up the tenths place.
• Since it's less than 5, you leave the tenths place as it is.

Hence, 0.13 rounds to 0.1 when expressed to the nearest tenth. This process is essential for achieving consistency and accuracy while dealing with decimals.