### You'd think that a Bill Gates application would be able to handle large numbers

Some people can wiggle their ears. I can recite powers of 2 up to about 8,192 or so. I can't necessarily tell you that 4,096 is 2 to the twelfth power, but I can multiply the numbers. (I used to be able to go up to 65,536, but I can't do that any more. Age, I guess.)

As a result of a drunken bet with Catherine Zeta-Jones on the deck of the Edmund Fitzgerald -

Strike that. It's not true, but it sounds better that way.

As a result of an inane conversation with co-workers, I was going to multiply powers of two all the way up to two to the 8,192nd power. Using Microsoft Excel, I got all the way to two to the 49th power:

But then I looked at the number for two to the 50th power:

As Devo would say, It's Not Right. But Excel was not meant to be a high-powered scientific calculator:

Returning to the title of this post, the precision in Excel is good enough for Bill and Melinda to maintain their household budget. I don't think they'll become quadrillionaires any time soon.

As a result of a drunken bet with Catherine Zeta-Jones on the deck of the Edmund Fitzgerald -

Strike that. It's not true, but it sounds better that way.

As a result of an inane conversation with co-workers, I was going to multiply powers of two all the way up to two to the 8,192nd power. Using Microsoft Excel, I got all the way to two to the 49th power:

*2*

4

8

16

32

64

128

256

512

1,024

2,048

4,096

8,192

16,384

32,768

65,536

131,072

262,144

524,288

1,048,576

2,097,152

4,194,304

8,388,608

16,777,216

33,554,432

67,108,864

134,217,728

268,435,456

536,870,912

1,073,741,824

2,147,483,648

4,294,967,296

8,589,934,592

17,179,869,184

34,359,738,368

68,719,476,736

137,438,953,472

274,877,906,944

549,755,813,888

1,099,511,627,776

2,199,023,255,552

4,398,046,511,104

8,796,093,022,208

17,592,186,044,416

35,184,372,088,832

70,368,744,177,664

140,737,488,355,328

281,474,976,710,656

562,949,953,421,3124

8

16

32

64

128

256

512

1,024

2,048

4,096

8,192

16,384

32,768

65,536

131,072

262,144

524,288

1,048,576

2,097,152

4,194,304

8,388,608

16,777,216

33,554,432

67,108,864

134,217,728

268,435,456

536,870,912

1,073,741,824

2,147,483,648

4,294,967,296

8,589,934,592

17,179,869,184

34,359,738,368

68,719,476,736

137,438,953,472

274,877,906,944

549,755,813,888

1,099,511,627,776

2,199,023,255,552

4,398,046,511,104

8,796,093,022,208

17,592,186,044,416

35,184,372,088,832

70,368,744,177,664

140,737,488,355,328

281,474,976,710,656

562,949,953,421,312

But then I looked at the number for two to the 50th power:

*1,125,899,906,842,620*As Devo would say, It's Not Right. But Excel was not meant to be a high-powered scientific calculator:

*Numeric Precision*

Microsoft Excel [was] developed to compete in the business software market where precision is probably not important for simple calculations. However many of the real-world calculations used in computational science require many digits of precision to the right of the decimal point.

Excel's maintains an internal numeric precision of 15 digits. By comparison a typical scientific calculator displays 10 digits but probably stores 12 digits while a CRAY 1 supercomputer has 15 digits in single-precision, floating point number. Excel stores 15 digits internally, but rounds the value for the screen display according to the format of the cell.

Numeric Range

Numeric range determines the sensitivity of the spreadsheet to overflow and underflow errors. Excel stores numbers between -1.798 x10 +308 and 1.798 x 10+308 for a numeric range of ±10+308. A scientific calculator handles a range of 10±99 and the CRAY 1 has a range of 10±2500. Although the largest number that Excel can store is 1.798 x 10+308, the largest number that you can type is 9.999 x 10+307. If you type in a larger number, Excel will treat it as a character string.

Most computational science calculations have reasonable results somewhere in the range of 10-40 to 10+40. When these numbers are used in an equation, the intermediate results are often quite large. If the intermediate results exceed the range of the computer then an overflow condition will return an error.Microsoft Excel [was] developed to compete in the business software market where precision is probably not important for simple calculations. However many of the real-world calculations used in computational science require many digits of precision to the right of the decimal point.

Excel's maintains an internal numeric precision of 15 digits. By comparison a typical scientific calculator displays 10 digits but probably stores 12 digits while a CRAY 1 supercomputer has 15 digits in single-precision, floating point number. Excel stores 15 digits internally, but rounds the value for the screen display according to the format of the cell.

Numeric Range

Numeric range determines the sensitivity of the spreadsheet to overflow and underflow errors. Excel stores numbers between -1.798 x10 +308 and 1.798 x 10+308 for a numeric range of ±10+308. A scientific calculator handles a range of 10±99 and the CRAY 1 has a range of 10±2500. Although the largest number that Excel can store is 1.798 x 10+308, the largest number that you can type is 9.999 x 10+307. If you type in a larger number, Excel will treat it as a character string.

Most computational science calculations have reasonable results somewhere in the range of 10-40 to 10+40. When these numbers are used in an equation, the intermediate results are often quite large. If the intermediate results exceed the range of the computer then an overflow condition will return an error.

Returning to the title of this post, the precision in Excel is good enough for Bill and Melinda to maintain their household budget. I don't think they'll become quadrillionaires any time soon.

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