Number DigitDecimal in the thousandths place
-83.420 in Words
-83.420 is a negative terminating decimal. It has 3 decimal places, and its final digit is in the thousandths place.
Direct Answer
-83.420 in words is negative eighty-three point four two zero.
-83.420 has the same numerical value as -83.42, but it is written to the thousandths place.
-83.420 Place-Value Breakdown
The digits 8 and 3 form the whole-number part, while 4 in the tenth place, 2 in the hundredth place, and 0 in the thousandth place.
| Part | Digit | Place | Digit value |
|---|---|---|---|
| Whole part | 8 | tens | 80 |
| Whole part | 3 | ones | 3 |
| Decimal part | 4 | tenth | 4/10 |
| Decimal part | 2 | hundredth | 2/100 |
| Decimal part | 0 | thousandth | 0/1000 |
What Kind of Decimal Is -83.420?
-83.420 is a negative terminating decimal. It is written to the thousandths place.
Written precision: the final 1 zero records precision even though removing it does not change the numerical value.
Expanded Form of -83.420
-83.420 = -(80 + 3 + 4/10 + 2/100)
-83.420 = -(83 + 420/1000)
-83.420 = -83 21/50
-83.420 = -83420/1000
The nonzero terms determine the numerical value, while the trailing zero preserves the written thousandths precision.
How -83.420 Simplifies to -4171/50
-83.420 = -83420/1000
The greatest common divisor of 83420 and 1000 is 20.
-83420 ÷ 20 = -4171
1000 ÷ 20 = 50
Therefore, -83420/1000 = -4171/50.
As a mixed fraction, the value is -83 21/50.
-83.420 as a Percentage
To convert -83.420 to a percentage, multiply it by 100.
-83.420 × 100 = -8342
Therefore, -83.420 = -8342%.
A Familiar Fraction Equivalent
The reduced form -4171/50 is a commonly used fraction. The decimal form is convenient for calculation, while the fraction shows the exact part-to-whole relationship.
Trailing Zeros and Written Precision
The final 1 zero does not change the numerical value, but it shows that -83.420 was written to the thousandths place.
Whole Part and Fractional Part
This mixed decimal combines the whole part 83 with the fractional part 420/1000. In place-value words, "and" marks that boundary.
How the Negative Sign Changes the Reading
Say "negative" once before the complete word form. The sign changes the direction and value, but it does not change the decimal places or the fraction-reduction steps.
-83.420 on a Number Line
-83.420 lies between -84 and -83. It is 0.58 above -84 and 0.42 below -83.
-83.420 Compared with Similar Decimals
| Decimal | Spoken form | Place-value form | Fraction | Percentage | Relationship |
|---|---|---|---|---|---|
| -8.342 | negative eight point three four two | negative eight and three hundred forty-two thousandths | -4171/500 | -834.2% | one tenth of -83.420 |
| -83.42 | negative eighty-three point four two | negative eighty-three and forty-two hundredths | -4171/50 | -8342% | same numerical value, fewer written decimal places |
| -83.420 | negative eighty-three point four two zero | negative eighty-three and four hundred twenty thousandths | -4171/50 | -8342% | current value |
| -83.4200 | negative eighty-three point four two zero zero | negative eighty-three and four thousand two hundred ten-thousandths | -4171/50 | -8342% | same numerical value, written to the ten-thousandths place |
| -834.2 | negative eight hundred thirty-four point two | negative eight hundred thirty-four and two tenths | -4171/5 | -83420% | ten times -83.420 |
Quick Practice
How is -83.420 read digit by digit?
Negative eighty-three point four two zero.
What is the place-value word form of -83.420?
Negative eighty-three and four hundred twenty thousandths.
What fraction is -83.420 in lowest terms?
-4171/50.
What percentage is equal to -83.420?
-8342%.
What is the absolute value of -83.420?
83.420.
Between which whole numbers does -83.420 lie?
Between -84 and -83.
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Frequently Asked Questions
How do you write -83.420 in words?
-83.420 in words is negative eighty-three point four two zero.
Why is -83.420 called negative eighty-three and four hundred twenty thousandths?
There are 3 digits after the point, so the fractional part is expressed in thousandths. Read the complete value as negative eighty-three and four hundred twenty thousandths.
What fraction is -83.420?
-83.420 is -83420/1000 exactly and -4171/50 in lowest terms.
Can -83420/1000 be simplified?
Yes. Divide its numerator and denominator by 20 to get -4171/50.
What percentage is -83.420?
-83.420 is equal to -8342%.
Is -83.420 the same as -83.4200?
Yes. -83.420 and -83.4200 have the same numerical value. However, -83.420 is written to the thousandths place, while -83.4200 is written to the ten-thousandths place and may communicate greater recorded precision.
Is -83.420 larger than -8.342?
No. Negative values reverse the comparison; -83.420 is ten times the value of -8.342.
What type of decimal is -83.420?
-83.420 is a negative terminating decimal. It is written to 3 decimal places and represents negative eighty-three and four hundred twenty thousandths.