Converting Between Standard and Expanded Form – Quiz
Numbers can be written in many different ways, and one of the most important is expanded form. Expanded form shows a number broken down into each of its place values. On the other hand, standard form is how we usually see numbers written, using just digits. In this post, we’ll learn how to convert between the two forms and practice doing it with some examples and a quiz.
What is Standard Form?
Standard form is the regular way of writing numbers using digits. For example, the number 73,241 is written in standard form. The digits (7, 3, 2, 4, and 1) each represent a certain value based on their place in the number.
- 7 is in the ten thousands place, so it means 70,000.
- 3 is in the thousands place, so it means 3,000.
- 2 is in the hundreds place, so it means 200.
- 4 is in the tens place, so it means 40.
- 1 is in the ones place, so it means 1.
When we put them all together, we get 73,241.
What is Expanded Form?
Expanded form is when you break down a number to show the value of each digit based on its place value. You write it as a sum of each digit’s value.
For example, the number 73,241 in expanded form is:
- 70,000 (because the 7 is in the ten thousands place)
- + 3,000 (because the 3 is in the thousands place)
- + 200 (because the 2 is in the hundreds place)
- + 40 (because the 4 is in the tens place)
- + 1 (because the 1 is in the ones place)
So, in expanded form, we write the number like this:
70,000 + 3,000 + 200 + 40 + 1
Why Do We Use Expanded Form?
Expanded form helps us understand what each digit in a number means. It breaks the number into smaller parts, which makes it easier to see how big a number is. This can be very useful when you’re working with large numbers.
Let’s take a big number like 90,731,319. When we break it down into expanded form, we can clearly see the value of each digit:
90,000,000 + 7,000,000 + 400,000 + 70,000 + 1,000 + 300 + 10 + 9
How to Convert Between Standard and Expanded Form
Now that we know what standard and expanded form are, let’s look at how to switch between them.
1. Converting from Expanded Form to Standard Form
To convert from expanded form to standard form, all you have to do is add the numbers together. Let’s use the example:
90,000,000 + 7,000,000 + 400,000 + 70,000 + 1,000 + 300 + 10 + 9
When you add these together, you get the number 97,471,319 in standard form.
2. Converting from Standard Form to Expanded Form
To convert a number from standard form to expanded form, you break it down by each digit’s place value. Let’s take 542,389 as an example:
- The 5 is in the hundred thousands place, so it means 500,000.
- The 4 is in the ten thousands place, so it means 40,000.
- The 2 is in the thousands place, so it means 2,000.
- The 3 is in the hundreds place, so it means 300.
- The 8 is in the tens place, so it means 80.
- The 9 is in the ones place, so it means 9.
So, 542,389 in expanded form would be written as:
500,000 + 40,000 + 2,000 + 300 + 80 + 9
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