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Word Problems

Browse Elementary Place Value
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Place value questions.
    Rounding numbers.
    Scientific notation.
    Significant figures/digits.

Decimal Places and Significant Figures [02/05/1999]
If a length of 5.738km is rounded to 5.7km, what is the accuracy?

Elapsed Time and the Grouping Factor [03/08/2003]
Why can't you just subtract the two times given in a word problem and get the time elapsed?

Lining Up Decimal Points [03/03/2003]
Why do we line up decimal points for addition and subtraction but not for division and multiplication?

Multiplying by a Power of Ten [10/31/2001]
Give the power of ten that the decimal must be multiplied by to eliminate the decimal point in the numbers: 3.825; 6.91; 19.207.

Numeration and Place Value [11/1/1994]
In the last 5 or 10 years, I have found an increase in the difficulty students have with place value and numeration and rounding. Is there some strategy, exercise, or drill to get these concepts across to kids, some manipulatives that could be used?

One Million Seconds [09/10/2001]
What is a million seconds in weeks, days, hours, minutes, and seconds? What does unit conversion have to do with number bases?

Place Value - Units Digit [03/22/1997]
What is the units digit of 6100?

Rounding 389.512 to Three Significant Digits [05/24/2003]
On the one hand, 390 is the closest multiple of 10 to 389.512; on the other hand, it is the closest whole number to 389.512.

Rounding Decimals [06/14/1999]
Is 1.9949 rounded to 2 decimal places 2.00 or 1.99?

Rounding Round Numbers [10/31/2016]
Two British teachers disagree about how to round 100 to one significant figure. By drawing out different interpretations of how to round such powers of ten, and quantities near them, Doctor Peterson emphasizes purpose and meaning over procedure and mechanical execution.

Rules for Significant Figures and Decimal Places [03/23/1999]
Accurate measurement: What are significant digits? When do we use them? Why?

What is a Significant Digit? [12/25/2001]
I came across a question asking for an answer with no more than "2 significant digits" - can you please explain what a significant digit is?

Which Place? [07/28/2003]
In which place is the digit 6 in the number 3164297 ?

Writing Commas in Numbers [07/11/2003]
Is it true that in France where we in America use decimals in math, they use commas, and where we use commas they use decimals?

1000 $1 Bills in 10 Envelopes [12/11/2002]
Put 1000 $1 bills into 10 envelopes in such a way that someone can ask you for any amount of money from $1 to $1000 and you can give it to him through a combination of the envelopes.

2421 and Only One [01/10/2017]
A teen sees valid representations in the 2421 coding system go unused. Doctor Peterson draws on complementarity to makes sense of how the system copes with redundancies.

2421 Decimal Code [11/08/2004]
Can you explain why some bit combinations for 2421 are invalid? For example, to represent decimal 5 (five) in 2421, the correct code is 1011. But why can't we represent decimal 5 in 2421 as 0101, because if we add the weights as 0*2 + 1*4 + 0*2 + 1*1, we get 5 in decimal.

4th Grade Estimation Problems [4/19/1996]
What types of problems exemplify using order of magnitude in estimation and compensation in estimation at the fourth grade level?

Are There Times When Following the Rounding Rules Isn't Best? [03/14/2007]
I have to estimate 32 - 15 by rounding the numbers to the nearest 10. I know 32 goes to 30, and rounding rules say 15 should go to 20. But that makes my estimated answer 10, when the real answer is 17. If I round the 15 to 10, I get an estimate of 20, which is closer to 17. Why does following the rounding rule give me a worse estimate?

Borrowing in Subtraction in Various Contexts [10/25/2006]
An explanation of using borrowing to calculate 12 5/11 minus 2 6/11 is extended to borrowing when subtracting times, liquid measures, and other wholes and parts in general.

Calculations Involving Significant Figures [02/22/2002]
My physics class is having a fair amount of trouble with significant digits.

Commas in Numbers [09/13/2001]
Do commas change the value of a number?

Comparing and Rounding Decimals [08/08/2001]
The length of each day of the year changes by about 0.000000002 s. Write a length of time that could be rounded up to this figure.

Converting Metric Measurements [11/03/2005]
I don't understand how to convert 50 millimeters into centimeters. Do I multiply 50 by 10 or divide it by 10? How do I decide?

Converting Negative Mixed Numbers to Improper Fractions [10/25/2006]
When converting a negative mixed number into an improper fraction, it seems like we ignore the rules for integer addition. For example, to convert -4 1/7 we think -4 1/7 = -4 * 7 + 1 = -28 + 1 = -27/7. But the correct answer is -29/7. How does -28 + 1 make -29?

Decimal Multiplication and Division [11/19/2002]
I'm tutoring a 6th-grade student, and I'm having a hard time explaining to her why you sometimes need to put a zero in the tenths place, in the quotient.

Decimal Numbers and Significant Figures [03/14/2007]
Correct 0.099 to 1 significant figure. Which one of the following is the answer, 0.1 or 0.10? Why?

Decoding Place Value [09/14/2003]
What do the different digits in a base 10 number mean?

Defining Decimal Numbers [07/01/2004]
An interesting look at how the idea of a 'decimal' number is widely misunderstood and the word itself is used incorrectly.

Different Techniques for Rounding Off Decimal Numbers [01/28/2006]
A discussion of some alternatives to the traditional rounding technique.

Dividing and Rounding [08/23/2001]
I have to answer a division problem and then round the quotient to the nearest hundredth...

Dividing by Powers of 10 [09/12/1998]
Can you explain how to move the decimal place when you divide by powers of 10?

Does 2k4 Mean 2004 or 2400? [01/10/2004]
On internet communities it is common to reduce figures using 'k' as a shortcut; for example 2k is used instead of 2000. I was under the impression that a number after the k (such as 2k4) meant 2400, and that to get 2004 in this system you'd need to write 2k004. But I've also seen 2k4 used for 2004. Which is correct? Does 2k4 mean 2004 or 2400?

Estimate the Sums [07/24/2003]
Use front-end estimation to estimate each sum: 428 + 219; 374 + 425.

Estimating Quotients [08/29/2001]
What is a valid estimation? Alternate ways of rounding off; significant digits.

Estimating Sums and Differences [10/11/2006]
When estimating sums and differences, I was taught to round each number to the greatest place value position of the smallest number. Is that correct, and can you show me how that works?

Estimating Sums By Rounding [08/16/1998]
Do you think my teacher means to round off after I get the answer, or before I add?

Estimation vs. Rounding [01/08/2002]
On our testing we have questions about estimating answers and rounding answers. The two methods give different answers. How are the two methods different?

Expanded and Standard Forms [09/06/1998]
What does it mean to write numbers in 'standard form' and 'expanded form'?

Explanation of Significant Figures [09/11/2007]
I'm confused about how to determine how many significant digits a given number has. Can you explain it?

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