Compare 7/100 and 0.7: Finding the Correct Mathematical Symbol

Question

Choose the missing sign (?):

7100?0.7 \frac{7}{100}?0.7

Video Solution

Solution Steps

00:00 Choose the appropriate sign
00:04 Convert a decimal fraction to a simple fraction
00:07 Place the digits in the numerator
00:10 Move the decimal point right until the number is whole and not decimal
00:13 We moved once, so the denominator will equal 10
00:19 Now we'll expand the fraction to the common denominator
00:22 Make sure to multiply both numerator and denominator
00:31 Now we'll place the fraction instead of the decimal fraction
00:36 Adjust the sign according to the numerators
00:39 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Convert the decimal 0.7 0.7 into a fraction for easy comparison.
  • Step 2: Compare the fractions 7100 \frac{7}{100} and 710 \frac{7}{10} using cross-multiplication.

Now, let's work through each step:
Step 1: Convert 0.7 0.7 to a fraction. Since 0.7=710 0.7 = \frac{7}{10} , we convert it to this fraction.
Step 2: Compare 7100 \frac{7}{100} and 710 \frac{7}{10} using cross-multiplication.
Calculate 7×10=70 7 \times 10 = 70 and 7×100=700 7 \times 100 = 700 .

Since 70<700 70 < 700 , it follows that 7100<710 \frac{7}{100} < \frac{7}{10} .

Therefore, the solution to the problem is << .

Answer

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