(c) MMIX = 1,000 + 1,000 + 9 = 2,009
(d) MMVI = 1,000 + 1,000 + 6 = 2,006
- The number three hundred two trillion, seventy billion, one hundred forty-nine
million, six thousand, one hundred ten looks like this as a decimal numeral:
302,070,149,006,110
Note the placement of the commas and the ciphers. Also note that we use the American
billion, which is equivalent to a thousand million.
- This is a slightly whimsical problem. You can add as many ciphers as you want to the
left of the digit 3 in the answer to the previous problem, and it does not change the
value of the number it represents. A mathematician might write it as
...,000,000,...,302,070,149,006,110
You can keep “attaching ciphers” forever in the left-hand direction!
- You can make any number in the decimal system ten times as large by adding one
cipher to its right and then repositioning the commas. Based on the numeral shown
for the answer to Prob. 4 above, you would get
3,020,701,490,061,100
If you want to make a number a hundred times as large, add two ciphers to its right and
then reposition the commas. Starting with the numeral shown for the answer to Prob. 4,
that gives you
30,207,014,900,611,000
If you want to make a number a thousand times as large, add three ciphers to its right and
then reposition the commas. Starting with the numeral shown for the answer to Prob. 4,
that gives you
302,070,149,006,110,000
- The number in the final answer to Prob. 6 would be written out in words as three
hundred two quadrillion, seventy trillion, one hundred forty-nine billion, six million,
one hundred ten thousand. That’s based on the United States terminology where a
billion is a thousand million, and a trillion is a million million.
- To solve this problem, tally the values of each digit in the decimal system and then add
them up, as follows.
- One times one gives you 1
- One times two gives you 2
- Zero times four gives you 0
Appendix B Worked-Out Solutions to Exercises: Chapters 11 to
