Problem 53 - Algebra 1: Concepts and Skills

Question

Write the numbers in order from least to greatest. (Skills Review p. 770) $$5.09,5.9,5.1,5.19,5.91$$

Step-by-Step Solution

Answer

The numbers in order from least to greatest are: 5.09, 5.1, 5.19, 5.9, 5.91.

Step 1: Understanding decimal numbers

The decimal system is based on the number 10. There are positions for tenths, hundredths, and thousandths and so on. Each value at a particular decimal position represents a portion of a whole number. To compare decimal numbers, start comparison from leftmost side known as the 'ones' place, moving to next place values on the right which are tenths, hundredths, etc. until a difference is noticed.

Step 2: Compare whole numbers

All given decimal numbers have the same whole number part which is 5. Hence, we can't order them yet. So, the next step is to compare the decimal parts.

Step 3: Compare the tenths

Looking at the first decimal place (tenths) we have 0, 9, 1, 1, and 9 respectively for the numbers 5.09, 5.9, 5.1, 5.19, 5.91. We can order them on the basis of tenths as following: 5.1, 5.19, 5.09, 5.9, 5.91.

Step 4: Compare the hundredths

Now 5.1 and 5.09 are in correct places. However, 5.19 and 5.9 as well as 5.9 and 5.91 need comparison. Upon comparing the hundredths place, 9 is bigger than 0, so 5.9 is greater than 5.19. Also, 5.91 has an extra hundredth which makes it bigger than 5.9. Therefore, the correct order is: 5.09, 5.1, 5.19, 5.9, 5.91.

Key Concepts

Ordering Numbers

Ordering decimal numbers might seem tricky at first, but it's all about examining each digit carefully. To arrange numbers from least to greatest, you'll need to start from the left, observing each place value.
First, look at the whole number part. If all numbers share the same whole number, move your attention to the decimals.

• Begin by comparing digits in the tenths place.
• Continue with the hundredths place if needed.

Think of it like reading a book from left to right, pausing when you see something different. This approach helps you line up each number in order.

Place Value

Understanding place value is crucial when dealing with decimal numbers. Place value helps you know the worth of the digit in relation to its position.
The places after the decimal point are ordered as tenths, hundredths, thousandths, and so forth.

• The first digit to the right of the decimal is the tenths place.
• The digit following the tenths is the hundredths place.
• This pattern continues with thousandths, ten-thousandths, etc.

Each step you move to the right decreases the value of the place by a factor of ten, making these places essential for detailed comparisons.

Comparing Decimals

Comparing decimals involves looking closely at each decimal place. Start from the leftmost non-zero digit and move right.
Check one place at a time until you find a difference.

• If the tenths digits are the same, move to the hundredths digits.
• If necessary, continue to the thousandths digits.

Remember, the smallest decimal is the one with zeros in more significant place values. By paying close attention to each place value, you can correctly determine which decimals are greater or lesser in value.