What Is 1.880726465 as a Fraction?
Converting a decimal like 1.880726465 into a fraction can seem tricky, but it’s a straightforward process with the right steps. Here’s a step-by-step explanation of how to express this number as a fraction:
Step 1: Recognize the Decimal
The number 1.880726465 is a decimal, where the integer part is 1, and the fractional part is 0.880726465.
Step 2: Eliminate the Decimal
To remove the decimal, count the number of digits after the decimal point. In this case, there are 9 digits: 880726465. Multiply both the decimal number and 1 (as a placeholder) by 109=1,000,000,00010^9 = 1,000,000,000. This gives:
1.880726465×1,000,000,000=1,880,726,4651.880726465 \times 1,000,000,000 = 1,880,726,465 1×1,000,000,000=1,000,000,0001 \times 1,000,000,000 = 1,000,000,000
Now, the number can be expressed as:
1.8807264651=1,880,726,4651,000,000,000\frac{1.880726465}{1} = \frac{1,880,726,465}{1,000,000,000}
Step 3: Simplify the Fraction
To simplify, find the greatest common divisor (GCD) of the numerator 1,880,726,4651,880,726,465 and the denominator 1,000,000,0001,000,000,000. The GCD of these two numbers is 5. Divide both the numerator and denominator by this value:
Simplified numerator: 1,880,726,4655=376,145,293\text{Simplified numerator: } \frac{1,880,726,465}{5} = 376,145,293 Simplified denominator: 1,000,000,0005=200,000,000\text{Simplified denominator: } \frac{1,000,000,000}{5} = 200,000,000
Thus, the fraction simplifies to:
376,145,293200,000,000\frac{376,145,293}{200,000,000}
Step 4: Verify the Simplified Fraction
Dividing the numerator by the denominator gives:
376,145,293÷200,000,000=1.880726465376,145,293 \div 200,000,000 = 1.880726465
This confirms the fraction is accurate.
Final Answer:
The decimal 1.880726465 as a fraction in its simplest form is:
376,145,293200,000,000\boxed{\frac{376,145,293}{200,000,000}}
This process illustrates how any repeating or non-repeating decimal can be converted into a fraction with clear, logical steps.
