Math / Numbers & Operations

QuestionIn order: $0.2,0.23,0.25,0.3,0.4$ Write the decimals in order starting with the smallest. $0.2,0.23,25 \%, \frac{3}{10}, \frac{2}{5}$
Write the original values in order. Exercise 6.3 Focus 1 Write these fractions in their simplest form. a $\frac{5}{10}$ $\square$ b $\frac{8}{20}$ $\square$ c $\frac{9}{12}$ $\square$

Studdy Solution

STEP 1

What is this asking? We need to sort a bunch of numbers, some decimals, some fractions, and even a percent, from smallest to largest! Watch out! Don't be tricked by how the numbers first appear!
Make sure to convert everything to the same format so you can compare apples to apples.

STEP 2

1. Convert to Decimals
2. Sort the Decimals
3. Write the Original Values

STEP 3

Alright, let's convert everything to decimals!
We've got $0.2$ , $0.23$ , and $0.3$ already as decimals, awesome!

STEP 4

Now, $25\%$ is the same as $\frac{25}{100}$ , which is $0.25$ .
See how we divided $25$ by $100$ to get the decimal?
Percentages are always out of $100$ !

STEP 5

Next up, $\frac{3}{10}$ .
To turn this fraction into a decimal, we divide the numerator ( $3$ ) by the denominator ( $10$ ).
So, $\frac{3}{10} = 0.3$ .

STEP 6

Lastly, $\frac{2}{5}$ .
We can multiply both the numerator and denominator by $2$ to get an equivalent fraction with a denominator of $10$ : $\frac{2 \cdot 2}{5 \cdot 2} = \frac{4}{10}$ .
Now, we divide the numerator ( $4$ ) by the denominator ( $10$ ), giving us $0.4$ .

STEP 7

Okay, we've got all our decimals: $0.2$ , $0.23$ , $0.25$ , $0.3$ , and $0.4$ .
Now, let's sort them from smallest to largest!
Think of these like money - which amount would you rather have?

STEP 8

We can see that $0.2$ is the smallest, then $0.23$ , followed by $0.25$ .
Then comes $0.3$ , and finally $0.4$ .
See how we looked at the tenths place first, then the hundredths place to compare the numbers?

STEP 9

Now, we just need to write the original values in order, matching them with our sorted decimals.

STEP 10

$0.2$ stays as $0.2$ . $0.23$ stays as $0.23$ . $0.25$ was originally $25\%$ . $0.3$ was $\frac{3}{10}$ .
And $0.4$ came from $\frac{2}{5}$ .

STEP 11

The numbers in order from smallest to largest are: $0.2$ , $0.23$ , $25\%$ , $\frac{3}{10}$ , $\frac{2}{5}$ .

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Studdy Solution

STEP 1

What is this asking? We need to sort a bunch of numbers, some decimals, some fractions, and even a percent, from smallest to largest! Watch out! Don't be tricked by how the numbers first appear!
Make sure to convert everything to the same format so you can compare apples to apples.

STEP 2

1. Convert to Decimals
2. Sort the Decimals
3. Write the Original Values

STEP 3

Alright, let's convert everything to decimals!
We've got $0.2$ , $0.23$ , and $0.3$ already as decimals, awesome!

STEP 4

Now, $25\%$ is the same as $\frac{25}{100}$ , which is $0.25$ .
See how we divided $25$ by $100$ to get the decimal?
Percentages are always out of $100$ !

STEP 5

Next up, $\frac{3}{10}$ .
To turn this fraction into a decimal, we divide the numerator ( $3$ ) by the denominator ( $10$ ).
So, $\frac{3}{10} = 0.3$ .

STEP 6

Lastly, $\frac{2}{5}$ .
We can multiply both the numerator and denominator by $2$ to get an equivalent fraction with a denominator of $10$ : $\frac{2 \cdot 2}{5 \cdot 2} = \frac{4}{10}$ .
Now, we divide the numerator ( $4$ ) by the denominator ( $10$ ), giving us $0.4$ .

STEP 7

Okay, we've got all our decimals: $0.2$ , $0.23$ , $0.25$ , $0.3$ , and $0.4$ .
Now, let's sort them from smallest to largest!
Think of these like money - which amount would you rather have?

STEP 8

We can see that $0.2$ is the smallest, then $0.23$ , followed by $0.25$ .
Then comes $0.3$ , and finally $0.4$ .
See how we looked at the tenths place first, then the hundredths place to compare the numbers?

STEP 9

Now, we just need to write the original values in order, matching them with our sorted decimals.

STEP 10

$0.2$ stays as $0.2$ . $0.23$ stays as $0.23$ . $0.25$ was originally $25\%$ . $0.3$ was $\frac{3}{10}$ .
And $0.4$ came from $\frac{2}{5}$ .

STEP 11

The numbers in order from smallest to largest are: $0.2$ , $0.23$ , $25\%$ , $\frac{3}{10}$ , $\frac{2}{5}$ .

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Studdy Solution

STEP 1

What is this asking? We need to sort a bunch of numbers, some decimals, some fractions, and even a percent, from smallest to largest! Watch out! Don't be tricked by how the numbers first appear!Make sure to convert everything to the same format so you can compare apples to apples.

STEP 2

1. Convert to Decimals2. Sort the Decimals3. Write the Original Values

STEP 3

Alright, let's **convert** everything to decimals!We've got 0.20.20.2, 0.230.230.23, and 0.30.30.3 already as decimals, awesome!

STEP 4

Now, 25%25\%25% is the same as 25100\frac{25}{100}10025​, which is 0.250.250.25.See how we **divided** 252525 by 100100100 to get the decimal?Percentages are always out of 100100100!

STEP 5

Next up, 310\frac{3}{10}103​.To turn this fraction into a decimal, we **divide** the numerator (333) by the denominator (101010).So, 310=0.3\frac{3}{10} = 0.3103​=0.3.

STEP 6

STEP 7

Okay, we've got all our decimals: 0.20.20.2, 0.230.230.23, 0.250.250.25, 0.30.30.3, and 0.40.40.4.Now, let's **sort** them from smallest to largest!Think of these like money - which amount would you rather have?

STEP 8

We can see that 0.20.20.2 is the smallest, then 0.230.230.23, followed by 0.250.250.25.Then comes 0.30.30.3, and finally 0.40.40.4.See how we looked at the tenths place first, then the hundredths place to **compare** the numbers?

STEP 9

Now, we just need to write the original values in order, matching them with our sorted decimals.

STEP 10

0.20.20.2 stays as 0.20.20.2. 0.230.230.23 stays as 0.230.230.23. 0.250.250.25 was originally 25%25\%25%. 0.30.30.3 was 310\frac{3}{10}103​.And 0.40.40.4 came from 25\frac{2}{5}52​.

STEP 11

The numbers in order from smallest to largest are: 0.20.20.2, 0.230.230.23, 25%25\%25%, 310\frac{3}{10}103​, 25\frac{2}{5}52​.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We need to sort a bunch of numbers, some decimals, some fractions, and even a percent, from smallest to largest! Watch out! Don't be tricked by how the numbers first appear!
Make sure to convert everything to the same format so you can compare apples to apples.

1. Convert to Decimals
2. Sort the Decimals
3. Write the Original Values

Alright, let's convert everything to decimals!
We've got $0.2$ , $0.23$ , and $0.3$ already as decimals, awesome!

Now, $25\%$ is the same as $\frac{25}{100}$ , which is $0.25$ .
See how we divided $25$ by $100$ to get the decimal?
Percentages are always out of $100$ !

Next up, $\frac{3}{10}$ .
To turn this fraction into a decimal, we divide the numerator ( $3$ ) by the denominator ( $10$ ).
So, $\frac{3}{10} = 0.3$ .

Okay, we've got all our decimals: $0.2$ , $0.23$ , $0.25$ , $0.3$ , and $0.4$ .
Now, let's sort them from smallest to largest!
Think of these like money - which amount would you rather have?

We can see that $0.2$ is the smallest, then $0.23$ , followed by $0.25$ .
Then comes $0.3$ , and finally $0.4$ .
See how we looked at the tenths place first, then the hundredths place to compare the numbers?

$0.2$ stays as $0.2$ . $0.23$ stays as $0.23$ . $0.25$ was originally $25\%$ . $0.3$ was $\frac{3}{10}$ .
And $0.4$ came from $\frac{2}{5}$ .

The numbers in order from smallest to largest are: $0.2$ , $0.23$ , $25\%$ , $\frac{3}{10}$ , $\frac{2}{5}$ .